Let the population Nt 54 e013t For N in millions and t in y

Let the population N(t) = 5.4 e^-013t For N in millions and t in years since 1995. Give the 1995 population. Calculate (to 2 decimal places) how many years until the population reaches 3 times its initial size. What you does this occur?

Solution

N(t) = 5.4e^(0.013t)

gives population since 1995

So,

a) Population in 1995 , plug t=0

N(0) = 5.4 million

b) Population becom 3 times original : 3*5.4 million , find t:

5.4*3 =  5.4e^(0.013t)

3 = e^(0.013t)

take natural log on both sides:

ln(3) = 0.013t

t = ln(3)/0.013 = 84.51 yrs since 1995

year = 1995 +84.51 = 2080